A Linear Programming Problem Has Two Constraints 2X + 4Y

question 20

Multiple Choice

A linear programming problem has two constraints 2X + 4Y ≥ 100 and 1X + 8Y ≤ 100, plus nonnegativity constraints on X and Y. Which of the following statements about its feasible region is true?

• A) There are four corner points including (50, 0) and (0, 12.5).
• B) The two corner points are (0, 0) and (50, 12.5).
• C) The graphical origin (0, 0) is in the feasible region.
• D) The feasible region is triangular in shape, bounded by (50, 0), (33-1/3, 8-1/3), and (100, 0).
• E) The feasible region cannot be determined without knowing whether the problem is to be minimized or maximized.

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Definitions:

Break-Even Point

The sales level at which total revenues equal total costs, resulting in neither profit nor loss.

Fixed Costs

Costs that do not change with the level of production or sales over a certain range and period, such as rent, salaries, and insurance premiums.

Unit Contribution Margin

The amount by which the selling price of a unit exceeds its variable costs, contributing to covering fixed costs and generating profit.

Selling Price

The amount for which a product or service is sold to the customer, determined by factors like cost, market demand, and competitive pricing.